Reconstruction of Gene Regulatory Networks based on Repairing Sparse Low-rank Matrices

Abstract

With the growth of high-throughput proteomic data, in particular time series gene expression data from various perturbations, a general question that has arisen is how to organize inherently heterogenous data into meaningful structures. Since biological systems such as breast cancer tumors respond differently to various treatments, little is known about exactly how these gene regulatory networks (GRNs) operate under different stimuli. For example, when we apply a drug-induced perturbation to a target protein, we often only know that the dynamic response of the specific protein may be affected. We do not know by how much, how long and even whether this perturbation affects other proteins or not. Challenges due to the lack of such knowledge not only occur in modeling the dynamics of a GRN but also cause bias or uncertainties in identifying parameters or inferring the GRN structure. This paper describes a new algorithm which enables us to estimate bias error due to the effect of perturbations and correctly identify the common graph structure among biased inferred graph structures. To do this, we retrieve common dynamics of the GRN subject to various perturbations. We refer to the task as "repairing" inspired by "image repairing" in computer vision. The method can automatically correctly repair the common graph structure across perturbed GRNs, even without precise information about the effect of the perturbations. We evaluate the method on synthetic data sets and demonstrate advantages over l1-regularized graph inference by advancing our understanding of how these networks respond across different targeted therapies. Also, we demonstrate an application to the DREAM data sets and discuss its implications to experiment design.